The present invention relates to an equalization technique useful for transmitting symbols of high-order constellations that are subject to corruption by inter-symbol interference and other data correlated noise (collectively, “ISI”). ISI refers to a variety of phenomena in data processing systems in which a data signal interferes with itself at a destination. The present invention also relates to the use of reliable symbols to determine values of source symbols that are corrupted by ISI. The present invention finds particular application in systems where source symbols are members of high-order constellations. Previously, such systems have required the use of training symbols for operation in the presence of real-world ISI phenomenon.
FIG. 1 illustrates an exemplary data processing system 100 in which ISI may occur. A source 110 may generate a data signal D (herein, a “source data signal”). When delivered to a destination 120 as a received signal X, the source data signal D may be corrupted by ISI sources within a channel 130. For example, multiple copies of a single data signal D may be captured at the destination 120, each copy being received with an unknown time shift and gain with respect to the other copies. Further, the time shifts and gains may vary over time.
ISI phenomena may be modeled mathematically. In the case where the data signal D is populated by a number of data symbols dn, captured signals xn at the destination 120 may be represented as:xn=a0·dn+f(dn−K2, . . . ,dn−1,dn+1, . . . ,dn+K1)+ωn  (1)where a0 represents a gain factor associated with the channel 130, f(dn−K2, . . . dn+K1) is a functional representation that relates the ISI to the symbols, dn−K2, . . . dn+K1, causing ISI corruption and ωn represents corruption from other sources. In linear systems, Equation 1 may reduce to:
                                          x            n                    =                                    d              n                        +                                          ∑                                                      i                    =                                          -                                              K                        1                                                                                                  i                    ≠                    0                                                                    K                  2                                            ⁢                                                a                  i                                ·                                  d                                      n                    -                    i                                                                        +                          ω              n                                      ,                            (        2        )            where a−k1, . . . ak2 represent impulse response of the channel. In accordance to common practice, the values ai have been normalized by the value of a0 in Equation 2.
ISI is seen as a serious impediment to the use of high-order constellations for data processing systems. A “constellation” is a set of unique values (constellation points) that may represent data symbols. Higher order constellations define a greater number of constellation points than lower order constellations. For example, symbols from a binary constellation, one having only two constellation points, can represent only a single digital bit per symbol. By contrast, symbols from an eight-point constellation, a sixteen-point constellation or a 256-point constellation can represent three, four or eight digital bits per symbol. At a common symbol rate, these higher order constellations can yield higher data throughput than lower order constellations.
Unfortunately, blind equalization (equalization without either an initial training sequence, or ‘refresher’ training sequences) is very hard to achieve with higher order constellations. The detrimental effects of ISI increase with increasing constellation order due to a greater contribution from the
      ∑                  i        =                  -                      K            1                              ⁢                          ⁢              i        ≠        0                    K      2        ⁢          ⁢            a      i        ·          d              n        -        i            term of Equation 2.
The inventors' co-pending patent application entitled, “Reliable Symbols as a Means of Improving the Performance of Information Transmission Systems,” filed Apr. 18, 2001 having Ser. No. 09/836,281, discloses several techniques for blind estimation of ISI in transmission systems using high-order constellations. The invention described herein and the work presented in the inventors' co-pending foreign applications are believed to be the first practical blind equalization techniques suitable for high-order constellation data systems. The inventors believe that the disclosures herein and the methods described in the co-pending patent applications enable an increased number of reliable symbols to be obtained from captured samples and that this increases the rate and effectiveness of equalization.